Monotonization of a Family of Implicit Schemes for the Burgers Equation

Alexander Kurganov () and Petr N. Vabishchevich ()
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Alexander Kurganov: Southern University of Science and Technology, Department of Mathematics
Petr N. Vabishchevich: Nuclear Safety Institute of the Russian Academy of Sciences

A chapter in Modeling, Simulation and Optimization of Complex Processes HPSC 2018, 2021, pp 247-256 from Springer

Abstract: Abstract We study numerical methods for convection-dominated fluid dynamics problems. In particular, we consider initial-boundary value problems for the Burgers equation with small diffusion coefficients. Our goal is to investigate several strategies, which can be used to monotonize numerical methods and to ensure non-oscillatory and positivity-preserving properties of the computed solutions. We focus on fully implicit finite-element methods constructed using the backward Euler time discretization combined with high-order spatial approximations. We experimentally study the following three monotonization approaches: mesh refinement, increasing the time-step size and utilizing higher-order finite-element approximations. Feasibility of these three strategies is demonstrated on a number of numerical examples for both one- and two-dimensional Burgers equations.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-55240-4_12

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DOI: 10.1007/978-3-030-55240-4_12

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